On matrix superpropagators. I

Given the free propagator of a matrix-valued field φαβ in the form <φαβ(x), φγδ (0)> = (1/2) (δαγδβδ +δαδδβγ − 2cδαβδγδ) Δ (x), we derive an integral representation for the matrix superpropagator <φαβN(x),φγδN(0)> for arbitrary N, and apply this to find the exponentially parametrized gravity superpropagator <|−g(x)|ωgαβ (x), |−g(0)|ωgγδ (0)> with gμν(x) ≡ [exp κφ(x)]μν. Other applications are also mentioned.